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Journal of Noncommutative Geometry最新文献

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Quantum geometry of Boolean algebras and de Morgan duality 布尔代数的量子几何与de Morgan对偶
IF 0.9 2区 数学
Journal of Noncommutative Geometry Pub Date : 2019-11-21 DOI: 10.4171/jncg/460
S. Majid
{"title":"Quantum geometry of Boolean algebras and de Morgan duality","authors":"S. Majid","doi":"10.4171/jncg/460","DOIUrl":"https://doi.org/10.4171/jncg/460","url":null,"abstract":"We take a fresh look at the geometrization of logic using the recently developed tools of `quantum Riemannian geometry' applied in the digital case over the field $Bbb F_2={0,1}$, extending de Morgan duality to this context of differential forms and connections. The 1-forms correspond to graphs and the exterior derivative of a subset amounts to the arrows that cross between the set and its complement. The line graph $0-1-2$ has a non-flat but Ricci flat quantum Riemannian geometry. The previously known four quantum geometries on the triangle graph, of which one is curved, are revisited in terms of left-invariant differentials, as are the quantum geometries on the dual Hopf algebra, the group algebra of $Bbb Z_3$. For the square, we find a moduli of four quantum Riemannian geometries, all flat, while for an $n$-gon with $n>4$ we find a unique one, again flat. We also propose an extension of de Morgan duality to general algebras and differentials over $Bbb F_2$.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49111416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Immersions and the unbounded Kasparov product: embedding spheres into Euclidean space 沉浸和无界卡斯帕罗夫积:将球体嵌入欧几里得空间
IF 0.9 2区 数学
Journal of Noncommutative Geometry Pub Date : 2019-11-14 DOI: 10.4171/jncg/451
W. D. Suijlekom, L. Verhoeven
{"title":"Immersions and the unbounded Kasparov product: embedding spheres into Euclidean space","authors":"W. D. Suijlekom, L. Verhoeven","doi":"10.4171/jncg/451","DOIUrl":"https://doi.org/10.4171/jncg/451","url":null,"abstract":"We construct an unbounded representative for the shriek class associated to the embeddings of spheres into Euclidean space. We equip this unbounded Kasparov cycle with a connection and compute the unbounded Kasparov product with the Dirac operator on $mathbb R^{n+1}$. We find that the resulting spectral triple for the algebra $C(mathbb S^n)$ differs from the Dirac operator on the round sphere by a so-called index cycle, whose class in $KK_0(mathbb C, mathbb C)$ represents the multiplicative unit. At all points we check that our construction involving the unbounded Kasparov product is compatible with the bounded Kasparov product using Kucerovsky's criterion and we thus capture the composition law for the shriek map for these immersions at the unbounded KK-theoretical level.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46126749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Explicit Rieffel induction module for quantum groups 量子群的显式Rieffel诱导模
IF 0.9 2区 数学
Journal of Noncommutative Geometry Pub Date : 2019-11-05 DOI: 10.4171/jncg/477
Damien Rivet
{"title":"Explicit Rieffel induction module for quantum groups","authors":"Damien Rivet","doi":"10.4171/jncg/477","DOIUrl":"https://doi.org/10.4171/jncg/477","url":null,"abstract":"For $mathbb{G}$ an algebraic (or more generally, a bornological) quantum group and $mathbb{B}$ a closed quantum subgroup of $mathbb{G}$, we build in this paper an induction module by explicitly defining an inner product which takes its value in the convolution algebra of $mathbb{B}$, as in the original approach of Rieffel cite{Rieffel}. In this context, we study the link with the induction functor defined by Vaes. In the last part we illustrate our result with parabolic induction of complex semi-simple quantum groups with the approach suggested by Clare cite{Clare}cite{CCH}.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41369412","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Hopf–Galois structures on ambiskew polynomial rings 双斜多项式环上的Hopf–Galois结构
IF 0.9 2区 数学
Journal of Noncommutative Geometry Pub Date : 2019-10-31 DOI: 10.4171/jncg/441
J. Bichon, Agust'in Garc'ia Iglesias
{"title":"Hopf–Galois structures on ambiskew polynomial rings","authors":"J. Bichon, Agust'in Garc'ia Iglesias","doi":"10.4171/jncg/441","DOIUrl":"https://doi.org/10.4171/jncg/441","url":null,"abstract":"We provide necessary and sufficient conditions to extend the Hopf-Galois algebra structure on an algebra R to a generalized ambiskew ring based on R, in a way such that the added variables for the extension are skew-primitive in an appropriate sense. We show that the associated Hopf algebra is again a a generalized ambiskew ring, based on a suitable Hopf algebra H(R). Several examples are examined, including the Hopf-Galois objects over Uq(sl2).","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42100679","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
The Novikov conjecture and extensions of coarsely embeddable groups Novikov猜想与粗可嵌入群的推广
IF 0.9 2区 数学
Journal of Noncommutative Geometry Pub Date : 2019-10-11 DOI: 10.4171/jncg/437
Jintao Deng
{"title":"The Novikov conjecture and extensions of coarsely embeddable groups","authors":"Jintao Deng","doi":"10.4171/jncg/437","DOIUrl":"https://doi.org/10.4171/jncg/437","url":null,"abstract":"Let $1 to N to G to G/N to 1$ be a short exact sequence of countable discrete groups and let $B$ be any $G$-$C^*$-algebra. In this paper, we show that the strong Novikov conjecture with coefficients in $B$ holds for such a group $G$ when the normal subgroup $N$ and the quotient group $G/N$ are coarsely embeddable into Hilbert spaces. As a result, the group $G$ satisfies the Novikov conjecture under the same hypothesis on $N$ and $G/N$.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48975738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
The coarse geometric $ell^p$-Novikov conjecture for subspaces of nonpositively curved manifolds 非点弯曲流形子空间的粗糙几何$ell^p$-Novikov猜想
IF 0.9 2区 数学
Journal of Noncommutative Geometry Pub Date : 2019-10-04 DOI: 10.4171/jncg/436
Lin Shan, Qin Wang
{"title":"The coarse geometric $ell^p$-Novikov conjecture for subspaces of nonpositively curved manifolds","authors":"Lin Shan, Qin Wang","doi":"10.4171/jncg/436","DOIUrl":"https://doi.org/10.4171/jncg/436","url":null,"abstract":"In this paper, we prove the coarse geometric $ell^p$-Novikov Conjecture for metric spaces with bounded geometry which admit a coarse embedding into a simply connected complete Riemannian manifold of nonpositive sectional curvature.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45129380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Koszul duality for compactly generated derived categories of second kind 第二类紧生派生范畴的Koszul对偶性
IF 0.9 2区 数学
Journal of Noncommutative Geometry Pub Date : 2019-09-25 DOI: 10.4171/jncg/438
Ai Guan, A. Lazarev
{"title":"Koszul duality for compactly generated derived categories of second kind","authors":"Ai Guan, A. Lazarev","doi":"10.4171/jncg/438","DOIUrl":"https://doi.org/10.4171/jncg/438","url":null,"abstract":"For any dg algebra $A$ we construct a closed model category structure on dg $A$-modules such that the corresponding homotopy category is compactly generated by dg $A$-modules that are finitely generated and free over $A$ (disregarding the differential). We prove that this closed model category is Quillen equivalent to the category of comodules over a certain, possibly nonconilpotent dg coalgebra, a so-called extended bar construction of $A$. This generalises and complements certain aspects of dg Koszul duality for associative algebras.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48778087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
$L^p$ coarse Baum–Connes conjecture and $K$-theory for $L^p$ Roe algebras L^p$ Roe代数的粗糙Baum-Connes猜想和K$-理论
IF 0.9 2区 数学
Journal of Noncommutative Geometry Pub Date : 2019-09-18 DOI: 10.4171/jncg/435
Jianguo Zhang, Dapeng Zhou
{"title":"$L^p$ coarse Baum–Connes conjecture and $K$-theory for $L^p$ Roe algebras","authors":"Jianguo Zhang, Dapeng Zhou","doi":"10.4171/jncg/435","DOIUrl":"https://doi.org/10.4171/jncg/435","url":null,"abstract":"In this paper, we verify the $L^p$ coarse Baum-Connes conjecture for spaces with finite asymptotic dimension for $pin[1,infty)$. We also show that the $K$-theory of $L^p$ Roe algebras are independent of $pin(1,infty)$ for spaces with finite asymptotic dimension.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42290712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
A proof of a conjecture of Shklyarov Shklyarov猜想的一个证明
IF 0.9 2区 数学
Journal of Noncommutative Geometry Pub Date : 2019-09-09 DOI: 10.4171/jncg/501
Michael K. Brown, M. Walker
{"title":"A proof of a conjecture of Shklyarov","authors":"Michael K. Brown, M. Walker","doi":"10.4171/jncg/501","DOIUrl":"https://doi.org/10.4171/jncg/501","url":null,"abstract":"We prove a conjecture of Shklyarov concerning the relationship between K. Saito's higher residue pairing and a certain pairing on the periodic cyclic homology of matrix factorization categories. Along the way, we give new proofs of a result of Shklyarov and Polishchuk-Vaintrob's Hirzebruch-Riemann-Roch formula for matrix factorizations.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46738118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
On localized signature and higher rho invariant of fibered manifolds 纤维流形的定域特征和高不变量
IF 0.9 2区 数学
Journal of Noncommutative Geometry Pub Date : 2019-08-28 DOI: 10.4171/jncg/426
Hongzhi Liu, Jinmin Wang
{"title":"On localized signature and higher rho invariant of fibered manifolds","authors":"Hongzhi Liu, Jinmin Wang","doi":"10.4171/jncg/426","DOIUrl":"https://doi.org/10.4171/jncg/426","url":null,"abstract":"Higher index of signature operator is a far reaching generalization of signature of a closed oriented manifold. When two closed oriented manifolds are homotopy equivalent, one can define a secondary invariant of the relative signature operator called higher rho invariant. The higher rho invariant detects the topological nonrigidity of a manifold. In this paper, we prove product formulas for higher index and higher rho invariant of signature operator on fibered manifolds. Our result implies the classical product formula for numerical signature of fiber manifolds obtained by Chern, Hirzebruch, and Serre in \"On the index of a fibered manifold\". We also give a new proof of the product formula for higher rho invariant of signature operator on product manifolds, which is parallel to the product formula for higher rho invariant of Dirac operator on product manifolds obtained by Xie and Yu in \"Positive scalar curvature, higher rho invariants and localization algebras\" and Zeidler in \"Positive scalar curvature and product formulas for secondary index invariants\".","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2019-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42775901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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